Abrasive particles having particular shapes and methods of forming such particles

ABSTRACT

An abrasive article includes a shaped abrasive particle including a body having a first height (h1) at a first end of the body defining a corner between an upper surface, a first side surface, and a second side surface, and a second height (h2) at a second end of the body opposite the first end defining an edge between the upper surface and a third side surface, wherein the average difference in height between the first height and the second height is at least about 50 microns. The body also includes a bottom surface defining a bottom area (A b ) and a cross-sectional midpoint area (A m ) defining an area of a plane perpendicular to the bottom area and extending through a midpoint of the particle, the body has an area ratio of bottom area to midpoint area (A b /A m ) of not greater than about 6.

CROSS-REFERENCE TO RELATED APPLICATION(S)

The present application is a continuation of U.S. Non-Provisional patentapplication Ser. No. 13/341,588, filed Dec. 30, 2011, entitled “AbrasiveParticles Having Particular Shapes and Methods of Forming SuchParticles,” naming inventors Doruk O. Yener et al., which claimspriority from U.S. Provisional Patent Application No. 61/428,912, filedDec. 31, 2010, entitled “Abrasive Particles Having Particular Shapes andMethods of Forming Such Particles,” naming inventors Jennifer H.Czerepinski et al., which application is incorporated by referenceherein in its entirety.

BACKGROUND

1. Field of the Disclosure

The following is directed to abrasive articles, and particularly,methods of forming abrasive particles.

2. Description of the Related Art

Abrasive particles and abrasive articles made from abrasive particlesare useful for various material removal operations including grinding,finishing, and polishing. Depending upon the type of abrasive material,such abrasive particles can be useful in shaping or grinding a widevariety of materials and surfaces in the manufacturing of goods. Certaintypes of abrasive particles have been formulated to date that haveparticular geometries, such as triangular shaped abrasive particles andabrasive articles incorporating such objects. See, for example, U.S.Pat. Nos. 5,201,916; 5,366,523; and 5,984,988.

Three basic technologies that have been employed to produce abrasiveparticles having a specified shape are (1) fusion, (2) sintering, and(3) chemical ceramic. In the fusion process, abrasive particles can beshaped by a chill roll, the face of which may or may not be engraved, amold into which molten material is poured, or a heat sink materialimmersed in an aluminum oxide melt. See, for example, U.S. Pat. No.3,377,660, disclosing a process comprising the steps of flowing moltenabrasive material from a furnace onto a cool rotating casting cylinder,rapidly solidifying the material to form a thin semisolid curved sheet,densifying the semisolid material with a pressure roll, and thenpartially fracturing the strip of semisolid material by reversing itscurvature by pulling it away from the cylinder with a rapidly drivencooled conveyor.

In the sintering process, abrasive particles can be formed fromrefractory powders having a particle size of up to 10 micrometers indiameter. Binders can be added to the powders along with a lubricant anda suitable solvent, e.g., water. The resulting mixtures, mixtures, orslurries can be shaped into platelets or rods of various lengths anddiameters. See, for example, U.S. Pat. No. 3,079,242, which discloses amethod of making abrasive particles from calcined bauxite materialcomprising the steps of (1) reducing the material to a fine powder, (2)compacting under affirmative pressure and forming the fine particles ofsaid powder into grain sized agglomerations, and (3) sintering theagglomerations of particles at a temperature below the fusiontemperature of the bauxite to induce limited recrystallization of theparticles, whereby abrasive grains are produced directly to size.

Chemical ceramic technology involves converting a colloidal dispersionor hydrosol (sometimes called a sol), optionally in a mixture, withsolutions of other metal oxide precursors, to a gel or any otherphysical state that restrains the mobility of the components, drying,and firing to obtain a ceramic material. See, for example, U.S. Pat.Nos. 4,744,802 and 4,848,041.

Still, there remains a need in the industry for improving performance,life, and efficacy of abrasive particles, and the abrasive articles thatemploy abrasive particles.

SUMMARY

According to a first aspect, an abrasive article includes an abrasiveparticle comprising a body having a base, an upper surface, and a sidesurface extending between the upper surface and base, wherein body has arake angle as defined by the angle between the side surface and the basewithin a range between about 1° and about 80°.

According to a second aspect, an abrasive article includes an abrasiveparticle comprising a body, wherein in an upright position the particlecomprises a tilted upper surface, and a height of the particle at afirst end is significantly different than a height of the particle at asecond end.

According to a third aspect, an abrasive article includes an abrasiveparticle comprising a body having a length (l), width (w), a firstheight (h1) and a second height (h2), wherein in an upright position,the first height and second height are separated from each other by thelength or the width of the body, and wherein the first height is atleast about 5% greater than the second height, wherein the heightdifference is calculate as Δh=[(h1−h2)/h1]×100%.

In yet another aspect, an abrasive article includes an abrasive particlecomprising a body having a length (l), width (w), and height (t),wherein l≧w≧h, wherein the body has a first height at a first end of theparticle, and a second height at a second end of the particle oppositethe first end, and the first height and the second height aresignificantly different from each other. The body also includes an uppersurface extending between the first end and the second end, wherein theupper surface having a curvilinear contour.

According to another aspect, a method of forming an abrasive articleincludes providing a mixture on a substrate, forming the mixture into ashaped abrasive particle comprising a body, wherein in an uprightposition the particle comprises a tilted upper surface, and a height ofthe particle at a first end is significantly different than a height ofthe particle at a second end.

In still another aspect, an abrasive article includes an abrasiveparticle having a body, wherein in an upright position the particlecomprises a tilted upper surface, and a height of the particle at afirst end is significantly different than a height of the particle at asecond end, wherein the tilted upper surface comprises a texture.

According to one particular aspect, an abrasive article includes ashaped abrasive particle including a body having a first height (h1) ata first end of the body defining a corner between an upper surface, afirst side surface, and a second side surface, and a second height (h2)at a second end of the body opposite the first end defining an edgebetween the upper surface and a third side surface, wherein the averagedifference in height between the first height and the second height isat least about 50 microns. The body includes a bottom surface defining abottom area (A_(b)), the body further comprising a cross-sectionalmidpoint area (A_(m)) defining an area of a plane perpendicular to thebottom area and extending through a midpoint of the particle, the bodycomprising an area ratio of bottom area to midpoint area (A_(b)/A_(m))of not greater than about 6.

In another certain aspect, an abrasive article comprises a shapedabrasive particle including a body having a length (l), a width (w), anda thickness (t), wherein the length≧width and the width≧thickness,wherein the body comprises a two-dimensional shape as viewed in a planedefined by the length and the width of the body selected from the groupconsisting of ellipsoids, Greek alphabet characters, Latin alphabetcharacters, Russian alphabet characters, triangles, pentagons, hexagons,heptagons, octagons, nonagons, decagons, and a combination thereof. Thebody comprises a first height (h1) at a first end of the body defining acorner between an upper surface, a first side surface, and a second sidesurface, and a second height (h2) at a second end of the body oppositethe first end defining an edge between the upper surface and a thirdside surface, wherein the average difference in height between the firstheight and the second height is at least about 50 microns.

For yet another aspect, an abrasive article comprises a shaped abrasiveparticle including a body having a length (l), a width (w), and athickness (t), wherein the length≧width and the width≧thickness, whereinthe body comprises a triangular two-dimensional shape as viewed in aplane defined by a length and a width of the body. The body comprises afirst height (h1) at a first end of the body defining a corner betweenan upper surface, a first side surface, and a second side surface, and asecond height (h2) at a second end of the body opposite the first enddefining an edge between the upper surface and a third side surface,wherein the average difference in height between the first height andthe second height is at least about 50 microns.

According to another aspect, an abrasive article comprises a shapedabrasive particle including a body having a first height (h1) at a firstend of the body defining a corner between an upper surface, a first sidesurface, and a second side surface, and a second height (h2) at a secondend of the body opposite the first end defining an edge between theupper surface and a third side surface, wherein the body comprises anormalized height difference defined by the equation [(h1−h2)/(h1/h2)]of at least about 40, wherein h1 is greater than h2. The body comprisesa base defining a bottom area (A_(b)), the body further comprising across-sectional midpoint area (A_(m)) defining an area of a planeperpendicular to the bottom area and extending through a midpoint of theparticle, the body comprising an area ratio of bottom area to midpointarea (A_(b)/A_(m)) of not greater than about 6.

Still, in one particular aspect, an abrasive article includes a sampleof shaped abrasive particle comprising a plurality of individual shapedabrasive particles, each shaped abrasive particle having a body having afirst height (h1) at a first end of the body and a second height (h2) ata second end of the body opposite the first end, wherein h1 and h2 aresignificantly different relative to each other, and wherein the samplecomprises a height variation of at least about 20. The body comprises abase defining a bottom area (A_(b)), the body further comprising across-sectional midpoint area (A_(m)) defining an area of a planeperpendicular to the bottom area and extending through a midpoint of theparticle, the body comprising an area ratio of bottom area to midpointarea (A_(b)/A_(m)) of not greater than about 6.

According to another aspect, an abrasive article includes an abrasiveparticle comprising a body having a base, an upper surface, and a sidesurface extending between the upper surface and base, wherein body has arake angle as defined by the angle between the side surface and the basewithin a range between about 1° and about 80°. The body comprises afirst height (h1) at a first end of the particle and a second height(h2) at a second end of the particle opposite the first end, and whereinthe first height and the second height are significantly different fromeach other. Additionally, the body comprises a base defining a bottomarea (A_(b)), the body further comprising a cross-sectional midpointarea (A_(m)) defining an area of a plane perpendicular to the bottomarea and extending through a midpoint of the particle, the bodycomprising an area ratio of bottom area to midpoint area (A_(b)/A_(m))of not greater than about 6.

In another aspect, an abrasive article comprises an abrasive particleincluding a body having a base, an upper surface, and a side surfaceextending between the upper surface and base, wherein body includes atwo-dimensional shape of a triangle, an area of the base of at leastabout 30% of the total area of the body, and a first height (h1) at afirst end of the particle and a second height (h2) at a second end ofthe particle opposite the first end, and wherein the first height andthe second height are significantly different from each other.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure may be better understood, and its numerousfeatures and advantages made apparent to those skilled in the art byreferencing the accompanying drawings.

FIG. 1 includes a perspective illustration of an abrasive particle inaccordance with an embodiment.

FIG. 2 includes a cross-sectional illustration of the abrasive particleof FIG. 1 in accordance with an embodiment.

FIG. 3 includes a cross-sectional illustration of the abrasive particleof FIG. 1 in accordance with an embodiment.

FIG. 4 includes a perspective view illustration of an abrasive particlein accordance with an embodiment.

FIG. 5 includes a cross-sectional illustration of an abrasive particleof FIG. 4 in accordance with an embodiment.

FIG. 6 includes a cross-sectional illustration of the abrasive particleof FIG. 4 in accordance with an embodiment.

FIG. 7 includes a cross-sectional illustration of the abrasive particleof FIG. 4 in accordance with an embodiment.

FIG. 8 includes a perspective view illustration of an abrasive particlein accordance with an embodiment.

FIG. 9 includes a perspective view illustration of an abrasive particlein accordance with an embodiment.

FIG. 10 includes a perspective view illustration of an abrasive particlein accordance with an embodiment.

FIG. 11 includes a diagram of a screen printing process for forming anabrasive particle in accordance with an embodiment.

FIG. 12A includes a perspective view illustration of an abrasiveparticle in accordance with an embodiment.

FIG. 12 B includes a cross-sectional illustration of a portion of theabrasive particle of FIG. 12A.

FIG. 13 includes a cross-sectional illustration of a coated abrasivearticle incorporating the abrasive particulate material in accordancewith an embodiment.

FIGS. 14A-14J provide profilometer scans of each of the shaped abrasiveparticles of shaped abrasive particles in accordance with an embodiment.

FIGS. 15A-15J provide profilometer scans of each of the shaped abrasiveparticles of shaped abrasive particles in accordance with an embodiment.

FIGS. 16A-16J provide profilometer scans of each of the shaped abrasiveparticles of conventional shaped abrasive particles.

FIGS. 17A-17J provide profilometer scans of each of the shaped abrasiveparticles of conventional shaped abrasive particles.

FIGS. 18A and 18B provide the test results of a single grit scratchingtest.

FIG. 19 includes a picture of shaped abrasive particles according to anembodiment.

DETAILED DESCRIPTION

The following is directed to abrasive articles, and more particularly,abrasive particles having particular features, such as polyhedralshapes, shaped surfaces, rake angles, and the like. Additionally, thefollowing details a method of forming such abrasive particles. Theabrasive particles according to the embodiments herein may beincorporated into abrasive articles, such as coated abrasives and/orbonded abrasives. Alternatively, the shaped abrasive particles of theembodiments herein may be utilized in free abrasive technologies,including for example grinding and/or polishing slurries.

FIG. 1 includes a perspective view illustration of an abrasive particlein accordance with an embodiment. As illustrated, the abrasive particle100 can have a three-dimensional shape including a body 101 having anupper surface 105 and a bottom surface 106 opposite the upper surface105. As further illustrated, the body 101 can be formed to have sidesurfaces 102, 103, 107, and 108 that extend between the upper surface105 and the bottom surface 106.

The abrasive particle 100 can be formed such that the body 101 includesa polycrystalline material. Notably, the polycrystalline material caninclude abrasive grains. For example, the abrasive particle 100 can bean agglomerate including a plurality of abrasive particles, grit, and/orgrains bonded to each other to form the body 101 of the abrasiveparticle 100. Suitable abrasive grains can include nitrides, oxides,carbides, borides, oxynitrides, oxyborides, diamond, and a combinationthereof. In particular instances, the abrasive grains can include anoxide compound or complex, such as aluminum oxide, zirconium oxide,titanium oxide, yttrium oxide, chromium oxide, strontium oxide, siliconoxide, and a combination thereof. In one particular instance, theabrasive particle 100 is formed such that the abrasive grains formingthe body 101 include alumina, and more particularly, may consistessentially of alumina.

The abrasive particles contained within the body 101 can bypolycrystalline and have an average particle size that is generally notgreater than about 100 microns. In other embodiments, the averageparticle size can be less, such as not greater than about 80 microns,not greater than about 50 microns, not greater than about 30 microns,not greater than about 20 microns, not greater than about 10 microns, oreven not greater than about 1 micron. Still, the average size of theabrasive grains contained within the body 101 can be at least about 0.01microns, such as at least about 0.05 microns, such as at least about0.08 microns, at least about 0.1 microns, or even at least about 1micron. It will be appreciated that the abrasive grains can have anaverage particle size within a range between any of the minimum andmaximum values noted above.

In accordance with certain embodiments, the abrasive particle can be acomposite article including at least two different types of abrasivegrains within the body 101. It will be appreciated that different typesof abrasive grains are abrasive grains having different compositionswith regard to each other. For example, the body 101 can be formed suchthat is includes at least two different types of abrasive grains,wherein the two different types of abrasive grains can be nitrides,oxides, carbides, borides, oxynitrides, oxyborides, diamond, and acombination thereof.

In accordance with an embodiment, the abrasive particle 100 can have anaverage particle size, as measured by the largest dimension measurableon the body 101, of at least about 100 microns. In fact, the abrasiveparticle 100 can have an average particle size of at least about 150microns, such as at least about 200 microns, at least about 300 microns,at least about 400 microns, at least about 500 microns, at least about600 microns, at least about 700 microns, at least about 800 microns, oreven at least about 900 microns. Still, the abrasive particle 100 canhave an average particle size that is not greater than about 5 mm, suchas not greater than about 3 mm, not greater than about 2 mm, or even notgreater than about 1.5 mm. It will be appreciated that the abrasiveparticle 100 can have an average particle size within a range betweenany of the minimum and maximum values noted above.

The abrasive particle 100 can be a particularly dense object. Forexample, the density of the abrasive particle 100 can be at least about90% of theoretical density. In other instances, the density of theabrasive particle 100 can be greater, such as at least about 92%, atleast about 95%, or even at least about 97% theoretical density.

As illustrated, the body 101 can have a length (l), a width (w), and aheight (h). In accordance with an embodiment, the body 101 can be formedsuch that the length≧width≧height. In particular instances, the body 101can be formed to have a primary aspect ratio, which is a ratio expressedas length:width, having a value of at least 1:1. In other instances, thebody 101 can be formed such that the primary aspect ratio (l:w) is atleast about 1.5:1, such as at least about 2:1, at least about 4:1, oreven at least about 5:1. Still, in other instances, the abrasiveparticle 100 can be formed such that the body has a primary aspect ratiothat is not greater than about 10:1, such as not greater than 9:1, notgreater than about 8:1, or even not greater than about 5:1. It will beappreciated that the body 101 can have a primary aspect ratio within arange between any of the ratios noted above. Furthermore, it will beappreciated that reference herein to a height is the maximum heightmeasurable of the abrasive particle. It will be described later that theabrasive particle may have different heights at different positionswithin the body 101 of the abrasive particle 100.

In addition to the primary aspect ratio, the abrasive particle 100 canbe formed such that the body 101 comprises a secondary aspect ratio,which can be defined as a ratio of width:height. In certain instances,the secondary aspect ratio can be within a range between about 5:1 andabout 1:3, such as between about 4:1 and about 1:2, or even betweenabout 3:1 and about 1:2.

In accordance with another embodiment, the abrasive particle 100 can beformed such that the body comprises a tertiary aspect ratio, defined bythe ratio length:height. The tertiary aspect ratio of the body 101 canbe within a range between about 10:1 and about 1.5:1, such as between8:1 and about 1.5:1, such as between about 6:1 and about 1.5:1, or evenbetween about 4:1 and about 1.5:1.

As illustrated in FIG. 1, the abrasive particle 100 can be formed suchthat it can have a three-dimensional shape, which can be a polyhedralparticle shape. Some suitable polyhedral particle shapes can includetetrahedrons, pentahedrons, hexahedrons, heptahedrons, octahedrons,nonahedron, decahedrons, and a combination thereof.

FIG. 2 includes a cross-sectional illustration of the abrasive particleof FIG. 1. As illustrated, the abrasive particle can have a generallypolygonal two-dimensional contour when viewed in a plane defined by thewidth and height (i.e., the plane AA in FIG. 1). Notably, the abrasiveparticle 100 can have a generally trapezoidal two-dimensional shape.Accordingly, the body 101 can have an upper surface 105 defining a firstwidth (w₁) and a base 106 defining a second width (w₂). As illustrated,the abrasive particle 100 can have a body 101, wherein the width of thebottom surface 106 (w₂) is greater than the width (w₁) of the uppersurface 105. In particular instances, the difference (Δw) between thewidth of the bottom surface 106 (w₂) and the width (w₁) of the uppersurface 105 can be at least about 5%, wherein the difference iscalculate as Δw=[(w₂−w₁)/w₂]×100%. In other embodiments, the differencein the width (Δw) can be greater, such that the difference between thefirst width (w₁) and the second width (w₂) can be at least about 1%,such as at least about 2%, at least about 3%, at least about 4%, atleast about 5%, at least about 7%, at least about 10%, at least about12%, or even at least about 15%. Still, in other embodiments, thedifference in the width (Δw) between the bottom surface 106 and uppersurface 105 can be not greater than about 80%, such as not greater thanabout 70%, not greater than about 60%, not greater than about 50%, notgreater than about 40%, or even not greater than about 30%. It will beappreciated that the difference between the width of the bottom surface106 and upper surface 105 can be within a range between any of theminimum and maximum percentages provided above.

Furthermore, it will be appreciated that the abrasive particle 100 canbe formed such that it has a generally trapezoidal two-dimensional shapeas viewed in a plane defined by the length (l) and the height (h), suchas illustrated in FIG. 3. As such, the two-dimensional shape of theabrasive particle 100 can have the same difference in width between thebottom surface 106 and upper surface 105 as viewed in a plane defined bythe length and the height.

As further illustrated in FIG. 2, the bottom surface 106 can be formedsuch that it has a greater surface area as compared to the upper surface105 of the body 101 of the abrasive particle 100. In accordance with anembodiment, the body 101 can have a bottom surface 106 that comprises atleast 30% of the total surface area of the body 101. In otherembodiments, the bottom surface 106 can comprise a greater percentage ofthe total surface area of the body 101, such as at least about 35%, atleast about 40%, at least about 45%, at least about 50%, or even atleast about 60%. Still, it will be appreciated that the bottom surface106 can account for not greater than about 90%, such as not greater thanabout 80%, or even not greater than about 75% of the total surface areaof the body 101. The bottom surface 106 can account for an amount of thetotal surface area of the body 101 within a range between any of theminimum and maximum percentages noted above.

Formation of an abrasive particle wherein the bottom surface 106 has agreater surface area as compared to the other surfaces (e.g., the uppersurface 105) can facilitate the formation of an abrasive particlecapable of preferential orientation in an upright position. Preferentialorientation into an upright position is reference to a position of theabrasive particle as illustrated in FIG. 1. That is, the abrasiveparticle 100 can be oriented such that the upper surface 105 is facingupward, and positioned in a cutting position to engage a workpiece forabrading applications.

The abrasive particle 100 can be formed such that it has an uprightorientation probability of at least 50%. That is, when the abrasiveparticle 100 is dropped from a known distance, based upon the shape ofthe abrasive particle 100, the particle preferentially aligns and isoriented in an upright position as illustrated in FIG. 1. In accordancewith an embodiment, the upright orientation probability of the abrasiveparticle 100 can be greater, such as at least about 50%, such as atleast about 55%, at least about 60%, at least about 70%, or even atleast about 80%. In particular instances, the upright orientationprobability of the abrasive particle can be not greater than about 99%,such as not greater than about 97%, or even at least not greater than95%. It will be appreciated that the upright orientation probability forthe abrasive particle 100 can be within a range between any of theminimum and maximum percentages noted above. Furthermore, formation ofan abrasive particle having such upright orientation probabilitiesfacilitates formation of abrasive articles, such as coated abrasives,wherein the abrasive particles are preferentially oriented for mostefficient abrading applications.

As further illustrated in FIG. 2, the abrasive particle 100 can beformed such that the side surfaces 107 and 102 extend between the uppersurface 105 and the bottom surface 106. As illustrated, the sidesurfaces 107 and 102 can be tapered relative to a vertical axis definedby the height, thus facilitating the trapezoidal two-dimensional shapeof the abrasive particle 100.

In other embodiments, the side surfaces 107 and 102 can have curvilinearshapes. For example, the surfaces 107 and 102 can have convex shapessuch as illustrated by the dotted line 115. In other embodiments, theside surfaces 107 and 102 can be formed to have a concave shape asillustrated by the dotted lines 120.

As further illustrated in FIG. 2, the abrasive particle 100 can beformed to have a particular rake angle 202, which can be defined as theangle between the side surface 102 and the bottom surface 106 relativeto a vertical axis 201. In accordance with an embodiment, the abrasiveparticle 100 can have a body 101 wherein the rake angle 202 can bewithin a range between 1° and about 80°. In other embodiments, the rakeangle can be within a range between about 5° and 55°, such as betweenabout 10° and about 50°, between about 15° and 50°, or even betweenabout 20° and 50°. Formation of an abrasive particle 100 having such arake angle can improve the abrading capabilities of the abrasiveparticle 100. Notably, the rake angle can be within a range between anytwo rake angles noted above.

The body 101 of the abrasive particle 100 can further include a rakeangle 203 as defined between the side surface 107 and the bottom surface106 relative to the vertical axis 201. In accordance with an embodiment,the rake angle 203 can be substantially the same as the rake angle 202.Still, in other embodiments, the rake angle 203 can be engineered to bedifferent than the rake angle 202. In fact, the rake angle 203 may beengineered to be significantly different than the take angle 202 tofacilitate certain particular wear characteristics and abrasivecapabilities of the abrasive particle 100.

FIG. 3 includes a cross-sectional view of the abrasive particle of FIG.1 as viewed in a plane defined by the length and the height (i.e, theplane BB as illustrated in FIG. 1). The abrasive particle 100 as viewedin a plane defined by the length (l) and the height (h) can have agenerally polygonal two-dimensional shape. In particular, the abrasiveparticle 100 can have a two-dimensional shape as viewed in the planedefined by the length and the height that is has a generally trapezoidalpolygonal shape.

Still, as illustrated, the upper surface 105 can have a curvilinearcontour. That is, the upper surface 105 of the abrasive particle 100 canbe tilted such that the abrasive particle has a greater height atdifferent locations within the abrasive particle. For example, heightdefined by the distance of the upper surface 105 from the bottom surface106 at the end 320 of the abrasive particle 100 is different as comparedto the height of the abrasive particle at an opposite end 322 of theabrasive particle 100. In fact, in particular instances, the uppersurface 105 of the abrasive particle can have a concave shape. Furtherdetails on such features are discussed in greater detail herein.

As further illustrated, the abrasive particle 100 can have a rake angle302 as defined between the side surface 101 and the bottom surface 106of the abrasive particle 100. The rake angle 302 can be substantiallythe same as the rake angle 202 described herein. In other instances, therake angle 302 can be significantly different than any other rake angledescribed in accordance with the embodiments herein. Still, the rakeangle 302 can have a value within a range between about 1° and about80°, such as between about 1° and about 70°, between about 1° and about60°, between about 5° and about 60°, between about 15° and 55°, betweenabout 10° and about 50°, between about 15° and 50°, or even betweenabout 20° and 50°.

Additionally, the abrasive particle 100 can be formed to have a rakeangle 303, defined as an angle between the side surface 108 and thebottom surface 106 of the abrasive particle 100. The rake angle 303 canbe the same as the rake angle 302. However, in particular embodiments,the rake angle 303 may be formed to be a significantly different angleas compared to the rake angle 302. Still, the rake angle 303 can have avalue within a range between about 1° and about 80°, such as betweenabout 1° and about 70°, between about 1° and about 60°, between about 5°and about 60°, such as between about 5° and 55°, between about 10° andabout 50°, between about 15° and 50°, or even between about 20° and 50°.Notably, the rake angle can be within a range between any two rakeangles noted above.

While not illustrated, it will be appreciated that the side surfaces 101and 108 can include the same features as side surfaces 107 and 102. Thatis, for example, the side surfaces 101 and 108 can have curvilinearcontours. Moreover, the curvilinear contours may be defined as concave,convex, or a combination thereof.

FIG. 4 includes a perspective view illustration of an abrasive particlein accordance with an embodiment. As illustrated, the abrasive particle400 includes an upper surface 405, a bottom surface 406 opposite theupper surface 405, and side surfaces 403, 402, 407, and 408, extendingbetween the upper surface 405 and bottom surface 406.

FIG. 5 includes a cross-sectional illustration of a portion of theabrasive particle of FIG. 4. Notably, the abrasive particle illustratedin FIG. 5 is a cross-sectional view of the abrasive particle 400 asviewed in a plane defined by the length (l) and the height (h) of theabrasive particle 400 (i.e., the plane CC of FIG. 4). According to oneembodiment, the abrasive particle 400 can have a first height (h₁) at afirst end 501 of the abrasive particle 400 and a second height (h₂) at asecond end 502 of the abrasive particle 400. In accordance with anembodiment, the first end 501 and second end 502 can be spaced apartfrom each other by substantially the full length (l) of the abrasiveparticle 400. In accordance with an embodiment, the first height (h₁)and the second height (h₂) can be significantly different from eachother. In more particular instances, the abrasive particle 400 can beformed such that the first height (h₁) and the second height (h₂) have adifference (Ah) of at least about 5%, wherein the height difference iscalculate as Δh=[(h₁−h₂)/h₁]×100%, wherein h₁ is the first height andthe h₂ is the second height, and the second height is less than thefirst height. Notably, the height difference (Δh) can be at least about8%, such as at least about 10%, at least about 15%, at least about 20%,at least about 40%, or even at least about 50%. Still, in otherembodiments, the abrasive particle 400 can be formed such that theheight difference (Δh) is not greater than about 98%, such as notgreater than about 95%, or even not greater than about 90%. The heightdifference can be within a range between any of the percentages notedabove.

According to a particular embodiment, the abrasive particle can have aheight (h₁) of at least about 100 microns. In fact, the abrasiveparticle 400 can have a height (h₁) of at least about 150 microns, suchas at least about 175 micron, at least about 200 microns, at least about250 microns, at least about 300 microns, at least about 400 microns, atleast about 500 microns, at least about 600 microns, or even at leastabout 700 microns. Still, the abrasive particle 400 can have a height(h₁) that is not greater than about 5 mm, such as not greater than about3 mm, not greater than about 2 mm, or even not greater than about 1.5mm. It will be appreciated that the abrasive particle 400 can have aheight (h₁) within a range between any of the minimum and maximum valuesnoted above.

As further illustrated, the upper surface 405 can be tilted, such thatit is angled relative to the bottom surface 406. In fact, the uppersurface 405 can define a non-parallel plane relative to the bottomsurface 406.

As further illustrated in FIG. 5, the side surfaces 403 and 408extending between the upper surface 405 and bottom surface 406 can havegenerally curvilinear contours. That is, side surfaces 403 and 408 havegenerally concave contours.

FIG. 6 includes a cross-sectional illustration of the abrasive particleof FIG. 4. In particular, FIG. 6 includes a cross-sectional illustrationas viewed in a plane defined by the width and height of the abrasiveparticle 400 (i.e., the plane AA of FIG. 4). Notably, the side surfaces407 and 402 extending between the upper surface 405 and bottom surface406 can have curvilinear contours. More particularly, the side surfaces407 and 402 can have concave contours.

FIG. 7 includes a cross-sectional illustration of a portion of theabrasive particle of FIG. 4. Notably, the cross-sectional illustrationof FIG. 7 is viewed in a plane defined by the length and width of theabrasive particle 400 (i.e., the plane BB in FIG. 4). In accordance withan embodiment, the abrasive particle 400 can be formed such that it hasa first width (w₁) at a first end 701 of the abrasive particle definedby the side surface 403. Additionally, the abrasive particle 400 can beformed such that it has a second width (w₂) at a second end 702 at theside surface 408 of the abrasive particle 400. Notably, the first end701 and second end 702 can be spaced apart by substantially the fulllength (l) of the abrasive particle 400.

The abrasive particle 400 can be formed such that the body has agenerally trapezoidal two-dimensional shape as viewed in the planedefined by the length and the width. As such, the abrasive particle 400can have a first width (w₁) that is significantly less than the secondwidth (w₂), wherein the first and second widths are space apart by thefull length of the abrasive particle 400.

In accordance with an embodiment, the abrasive particle 400 can beformed such that the first width (w₁) is different than the second width(w₂) by a difference (Δw) of at least about 2%, wherein the difference(Δw) can be calculated from the equation Δw=[(w₂−w₁)/w₂]×100%, whereinw₂ is greater than w₁. In other embodiments, the difference between (w₁)and (w₂) can be greater, such as least about 5%, at least about 8%, atleast about 10%, at least about 20%, at least about 30%, or even atleast about 40%. Still, the difference in widths (Δw) can be not greaterthan about 98%, not greater than about 95%, or even not greater thanabout 90%. The difference in the widths can be within a range betweenany of the percentages noted above.

According to a particular embodiment, the abrasive particle can have awidth (w₂) of at least about 100 microns. In fact, the abrasive particle400 can have a width (w₂) of at least about 150 microns, such as atleast about 175 micron, at least about 200 microns, at least about 250microns, at least about 300 microns, at least about 400 microns, atleast about 500 microns, at least about 600 microns, or even at leastabout 700 microns. Still, the abrasive particle 400 can have a width(w₂) that is not greater than about 5 mm, such as not greater than about3 mm, not greater than about 2 mm, or even not greater than about 1 mm.It will be appreciated that the abrasive particle 400 can have a width(w₂) within a range between any of the minimum and maximum values notedabove.

Furthermore, it will be appreciated that the greatest length of anyparticle formed according to the embodiments herein can have the samedimensions as noted above for the width (w₂).

FIG. 8 includes a perspective view illustration of an abrasive particlein accordance with an embodiment. As illustrated, the abrasive particle800 can include an upper surface 805, a bottom surface 806 opposite theupper surface 805, and side surfaces 803, 802, 804, and 807 extendingbetween and connecting the upper surface 805 and bottom surface 806. Inaccordance with an embodiment, the abrasive particle 800 can have anupper surface 805 including a texture 809. The texture 809 can include apattern defining an array of features. Some suitable examples offeatures can include protrusions, grooves, and a combination thereof.The protrusions and grooves defining the texture 809 can be arranged ina regular array. That is, the protrusions and grooves can define aregular and repeating arrangement of features with respect to each otherthat can have short range order and/or long-range order across the uppersurface 805. For example, the upper surface 805 can include grooves 810and protrusions 811, which extend in between each other and across theentire length of the upper surface 805 of the abrasive particle 800.Still, it will be appreciated that the grooves 810 and protrusions 811can extend for a portion of the total length of the upper surface 805.

In other instances, the texture can be defined by an irregulararrangement of features on the upper surface 805. For example, the uppersurface 805 can include randomly oriented and randomly positionedfeatures, such as grooves 810 and protrusions 811, such that no patternor order exists between the features.

In accordance with an embodiment, the grooves 810 and protrusions 811can be positioned relative to each other to create scalloped edges 815and 816. The scalloped edges 815 and 816 may facilitate improved cuttingcapabilities and friability of the abrasive particle 800. Other seriesand arrangement of features can be provided on the upper surface 805 tocreate edges between the upper surface 805 and side surfaces 803, 802,804, and 807 having certain features. That is, texturing of the uppersurface 805 can facilitate the formation of edges 815 and 816 havingparticular features that can improve the abrasive capabilities of theabrasive grain 800.

The foregoing has described an abrasive particle 800 having a texturedupper surface 805. However, it will be appreciated other surfaces of theabrasive particle can be textured, including for example, a side surface802 that is adjacent to and extends at an angle to the upper surface805. Moreover, one or more combination of surfaces of the abrasiveparticle 800 can be textured.

The embodiments herein have been directed to abrasive particles havingparticular shapes. While the foregoing has demonstrated abrasiveparticles having generally four sides as viewed in cross-section, otherpolyhedral shapes can be utilized, and such polyhedral shapes can haveparticular polygonal two-dimensional shapes. For example, the abrasiveparticles of embodiments herein can include abrasive particles havingtwo-dimensional shapes of triangles, quadrilaterals, pentagons,hexagons, heptagons, octagons, nonagons, and decagons. For example, FIG.9 includes a cross-sectional illustration of an abrasive particle 900having a generally quadrilateral, and more particularly, a rectangulartwo-dimensional shape, as viewed in a plane defined by the width and theheight. Alternatively, FIG. 10 includes a perspective view illustrationof an abrasive particle that can have a generally octagonaltwo-dimensional shape as viewed in a plane defined by the length andwidth.

Referring now to additional shaped abrasive particles, a shaped abrasiveparticle of an embodiment herein can have a body defined by a length(l), which can be the longest dimension of any side of the shapedabrasive particle, a width (w) defined as a longest dimension of theshaped abrasive particle through a midpoint of the shaped abrasiveparticle, and a thickness (t) defined as the shortest dimension of theshaped abrasive particle extending in a direction perpendicular to thelength and width. In specific instances, the length can be greater thanor equal to the width. Moreover, the width can be greater than or equalto the thickness.

Additionally, the body of the shaped abrasive particles can haveparticular two-dimensional shapes. For example, the body can have atwo-dimensional shape as viewed in a plane define by the length andwidth having a polygonal shape, ellipsoidal shape, a numeral, a Greekalphabet character, Latin alphabet character, Russian alphabetcharacter, complex shapes utilizing a combination of polygonal shapesand a combination thereof. Particular polygonal shapes includetriangular, rectangular, quadrilateral, pentagon, hexagon, heptagon,octagon, nonagon, decagon, any combination thereof.

FIG. 12A includes a perspective view illustration of an abrasiveparticle in accordance with an embodiment. Additionally, FIG. 12Bincludes a cross-sectional illustration of the abrasive particle of FIG.12A. The body 1201 includes an upper surface 1203 a bottom major surface1204 opposite the upper surface 1203. The upper surface 1203 and thebottom surface 1204 can be separated from each other by side surfaces1205, 1206, and 1207. As illustrated, the body 1201 of the shapedabrasive particle 1200 can have a generally triangular shape as viewedin a plane of the upper surface 1203 defined by the length (l) and width(w) of the body 1201. In particular, the body 1201 can have a length(l), a width (w) extending through a midpoint 1281 of the body 1201.

In accordance with an embodiment, the body 1201 of the shaped abrasiveparticle can have a first height (h1) at a first end of the body definedby a corner 1213. Notably, the corner 1213 may represent the point ofgreatest height on the body 1201. The corner can be defined as a pointor region on the body 1201 defined by the joining of the upper surface1203, and two side surfaces 1205 and 1207. The body 1201 may furtherinclude other corners, spaced apart from each other, including forexample corner 1211 and corner 1212. As further illustrated, the body1201 can include edges 1214, 1215, and 1216 that can separated from eachother by the corners 1211, 1212, and 1213. The edge 1214 can be definedby an intersection of the upper surface 1203 with the side surface 1206.The edge 1215 can be defined by an intersection of the upper surface1203 and side surface 1205 between corners 1211 and 1213. The edge 1216can be defined by an intersection of the upper surface 1203 and sidesurface 1207 between corners 1212 and 1213.

As further illustrated, the body 1201 can include a second height (h2)at a second end of the body, which defined by the edge 1214, and furtherwhich is opposite the first end defined by the corner 1213. The axis1250 can extend between the two ends of the body 1201. FIG. 12B is across-sectional illustration of the body 1201 along the axis 1250, whichcan extend through a midpoint 1281 of the body along the dimension ofwidth (w) between the ends of the body 1201.

In accordance with an embodiment, the shaped abrasive particles of theembodiments herein, including for example, the particle of FIGS. 12A and12B can have an average difference in height, which is a measure of thedifference between h1 and h2. More particularly, the average differencein height can be calculated based upon a plurality of shaped abrasiveparticles from a sample. The sample can include a representative numberof shaped abrasive particles, which may be randomly selected from abatch, such as at least 8 particles, or even at least 10 particles. Abatch can be a group of shaped abrasive particles that are produced in asingle forming process, and more particularly, in the same, singleforming process. The average difference can be measured via using a STIL(Sciences et Techniques Industrielles de la Lumiere—France) MicroMeasure 3D Surface Profilometer (white light (LED) chromatic aberrationtechnique).

In particular instances, the average difference in height [h1-h2],wherein h1 is greater, can be at least about 50 microns. In still otherinstances, the average difference in height can be at least about 60microns, such as at least about 65 microns, at least about 70 microns,at least about 75 microns, at least about 80 microns, at least about 90microns, or even at least about 100 microns. In one non-limitingembodiment, the average difference in height can be not greater thanabout 300 microns, such as not greater than about 250 microns, notgreater than about 220 microns, or even not greater than about 180microns. It will be appreciated that the average difference in heightcan be within a range between any of the minimum and maximum valuesnoted above.

Moreover, the shaped abrasive particles herein, including for examplethe particle of FIGS. 12A and 12B, can have a profile ratio of averagedifference in height [h1−h2] to profile length (l_(p)) of the shapedabrasive particle, defined as [(h1−h2)/(l_(p))] of at least about 0.04.It will be appreciated that the profile length of the body can be alength of the scan across the body used to generate the data of h1 andh2 between opposite ends of the body. Moreover, the profile length maybe an average profile length calculated from a sample of multipleparticles that are measured. In certain instances, the profile length(l_(p)) can be the same as the width as described in embodiments herein.According to a particular embodiment, the profile ratio can be at leastabout 0.05, at least about 0.06, at least about 0.07, at least about0.08, or even at least about 0.09. Still, in one non-limitingembodiment, the profile ratio can be not greater than about 0.3, such asnot greater than about 0.2, not greater than about 0.18, not greaterthan about 0.16, or even not greater than about 0.14. It will beappreciated that the profile ratio can be within a range between any ofthe minimum and maximum values noted above.

Moreover, the shaped abrasive particles of the embodiments herein,including for example, the body 1201 of the particle of FIGS. 12A and12B can have a bottom surface 1204 defining a bottom area (A_(b)). Inparticular instances the bottom surface 1204 can be the largest surfaceof the body 1201. The bottom surface can have a surface area defined asthe bottom area (A_(b)) that is greater than the surface area of theupper surface 1203. Additionally, the body 1201 can have across-sectional midpoint area (A_(m)) defining an area of a planeperpendicular to the bottom area and extending through a midpoint 1281of the particle. In certain instances, the body 1201 can have an arearatio of bottom area to midpoint area (A_(b)/A_(m)) of not greater thanabout 6. In more particular instances, the area ratio can be not greaterthan about 5.5, such as not greater than about 5, not greater than about4.5, not greater than about 4, not greater than about 3.5, or even notgreater than about 3. Still, in one non-limiting embodiment, the arearatio may be at least about 1.1, such as at least about 1.3, or even atleast about 1.8. It will be appreciated that the area ratio can bewithin a range between any of the minimum and maximum values notedabove.

In accordance with one embodiment, the shaped abrasive particles of theembodiments herein, including for example, the particle of FIGS. 12A and12B can have a normalized height difference of at least about 40. Thenormalized height difference can be defined by the equation[(h1−h2)/(h1/h2)], wherein h1 is greater than h2. In other embodiments,the normalized height difference can be at least about 43, at leastabout 46, at least about 50, at least about 53, at least about 56, atleast about 60, at least about 63, or even at least about 66. Still, inone particular embodiment, the normalized height difference can be notgreater than about 200, such as not greater than about 180, not greaterthan about 140, or even not greater than about 110.

In another embodiment, the shaped abrasive particles herein, includingfor example, the particle of FIGS. 12A and 12B can have a heightvariation. Without wishing to be tied to a particular theory, it isthought that a certain height variation between shaped abrasiveparticles, can improve variety of cutting surfaces, and may improvegrinding performance of an abrasive article incorporating the shapedabrasive particles herein. The height variation can be calculated as thestandard deviation of height difference for a sample of shaped abrasiveparticles. In one particular embodiment, the height variation of asample can be at least about 20. For other embodiments, the heightvariation can be greater, such as at least about 22, at least about 24,at least about 26, at least about 28, at least about 30, at least about32, or even at least about 34. Still, in one non-limiting embodiment,the height variation may be not greater than about 180, such as notgreater than about 150, or even not greater than about 120. It will beappreciated that the height variation can be within a range between anyof the minimum and maximum values noted above.

According to another embodiment, the shaped abrasive particles herein,including for example the particles of FIGS. 12A and 12B can have anellipsoidal region 1217 in the upper surface 1203 of the body 1201. Theellipsoidal region 1217 can be defined by a trench region 1218 that canextend around the upper surface 1203 and define the ellipsoidal region1217. The ellipsoidal region 1217 can encompass the midpoint 1281.Moreover, it is thought that the ellipsoidal region 1217 defined in theupper surface can be an artifact of the forming process, and may beformed as a result of the stresses imposed on the mixture duringformation of the shaped abrasive particles according to the methodsdescribed herein.

Moreover, the rake angle described in accordance with other embodimentsherein can be applicable to the body 1201. Likewise, all other featuresdescribed herein, such as the contours of side surfaces, upper surfaces,and bottom surfaces, the upright orientation probability, primary aspectratio, secondary aspect ratio, tertiary aspect ratio, and composition,can be applicable to the exemplary shaped abrasive particle illustratedin FIGS. 12A and 12B.

While the foregoing features of height difference, height variation, andnormalized height difference have been described in relation to theabrasive particle of FIGS. 12A and 12B, it will be appreciated that suchfeatures can apply to any other shaped abrasive particles describedherein, including for example, abrasive particles having a substantiallytrapezoidal two-dimensional shape.

The shaped abrasive particles of the embodiments herein may include adopant material, which can include an element or compound such as analkali element, alkaline earth element, rare earth element, hafnium,zirconium, niobium, tantalum, molybdenum, vanadium, or a combinationthereof. In one particular embodiment, the dopant material includes anelement or compound including an element such as lithium, sodium,potassium, magnesium, calcium, strontium, barium, scandium, yttrium,lanthanum, cesium, praseodymium, niobium, hafnium, zirconium, tantalum,molybdenum, vanadium, chromium, cobalt, iron, germanium, manganese,nickel, titanium, zinc, and a combination thereof.

In certain instances, the shaped abrasive particles can be formed tohave a specific content of dopant material. For example, the body of ashaped abrasive particle may include not greater than about 12 wt % forthe total weight of the body. In other instances, the amount of dopantmaterial can be less, such as not greater than about 11 wt %, notgreater than about 10 wt %, not greater than about 9 wt %, not greaterthan about 8 wt %, not greater than about 7 wt %, not greater than about6 wt %, or even not greater than about 5 wt % for the total weight ofthe body. In at least one non-limiting embodiment, the amount of dopantmaterial can be at least about 0.5 wt %, such at least about 1 wt %, atleast about 1.3 wt %, at least about 1.8 wt %, at least about 2 wt %, atleast about 2.3 wt %, at least about 2.8 wt %, or even at least about 3wt % for the total weight of the body. It will be appreciated that theamount of dopant material within the body of the shaped abrasiveparticle can be within a range between any of the minimum or maximumpercentages noted above.

FIG. 13 includes a cross-sectional illustration of a coated abrasivearticle incorporating the abrasive particulate material in accordancewith an embodiment. As illustrated, the coated abrasive 1300 can includea substrate 1301 and a make coat 1303 overlying a surface of thesubstrate 1301. The coated abrasive 1300 can further include abrasiveparticulate material 1306. The abrasive particulate material can includea first type of shaped abrasive particle 1305, a second type of abrasiveparticulate material 1307 in the form of diluent abrasive particleshaving a random shape, which may not necessarily be shaped abrasiveparticles. The coated abrasive 1300 may further include size coat 1304overlying and bonded to the abrasive particulate materials 1305, 1306,1307, and the make coat 1304.

According to one embodiment, the substrate 1301 can include an organicmaterial, inorganic material, and a combination thereof. In certaininstances, the substrate 1301 can include a woven material. However, thesubstrate 1301 may be made of a non-woven material. Particularlysuitable substrate materials can include organic materials, includingpolymers, and particularly, polyester, polyurethane, polypropylene,polyimides such as KAPTON from DuPont, paper. Some suitable inorganicmaterials can include metals, metal alloys, and particularly, foils ofcopper, aluminum, steel, and a combination thereof.

The make coat 1303 can be applied to the surface of the substrate 1301in a single process, or alternatively, the abrasive particulatematerials 1306 can be combined with a make coat 1303 material andapplied as a mixture to the surface of the substrate 1301. Suitablematerials of the make coat 1303 can include organic materials,particularly polymeric materials, including for example, polyesters,epoxy resins, polyurethanes, polyamides, polyacrylates,polymethacrylates, polyvinyl chlorides, polyethylene, polysiloxane,silicones, cellulose acetates, nitrocellulose, natural rubber, starch,shellac, and mixtures thereof. In one embodiment, the make coat 1303 caninclude a polyester resin. The coated substrate can then be heated inorder to cure the resin and the abrasive particulate material to thesubstrate. In general, the coated substrate 1301 can be heated to atemperature of between about 100° C. to less than about 250° C. duringthis curing process.

The abrasive particulate material 1306 can include shaped abrasiveparticles according to embodiments herein. In particular instances, theabrasive particulate material 1306 may include different types of shapedabrasive particles. The different types of shaped abrasive particles candiffer from each other in composition, two-dimensional shape,three-dimensional shape, size, and a combination thereof as described inthe embodiments herein. As illustrated, the coated abrasive 1300 caninclude shaped abrasive particles 1305 having a generally triangulartwo-dimensional shape according to shaped abrasive particles describedin embodiments herein.

The other type of abrasive particles 1307 can be diluent particlesdifferent than the shaped abrasive particles 1305. For example, thediluent particles can differ from the shaped abrasive particles 1305 incomposition, two-dimensional shape, three-dimensional shape, size, and acombination thereof. For example, the abrasive particles 1307 canrepresent conventional, crushed abrasive grit having random shapes. Theabrasive particles 1307 may have a median particle size less than themedian particle size of the shaped abrasive particles 1305.

In particular instances, as illustrated in FIG. 13, a plurality of theshaped abrasive particles 1305 in the abrasive article 1300 can beoriented in the same manner. Notably, the shaped abrasive particles 1305can have an upright orientation, wherein the particles are resting ontheir respective bottom surfaces, which are the largest surface arearegions, and the upper surface defining the ends of different height, ispointing away from the substrate 1301 and configured to contact aworkpiece to conduct a material removal process. More particularly, theshaped abrasive particles 1305 can have an upright orientation whereinthe bottom surface is in direct contact with the make coat 1303, and theupper surface of the shaped abrasive particles is in direct contact withan overlying coat, such as a size coat 1309. In accordance with anembodiment, a majority of the shaped abrasive particles 1305 within theabrasive article 1300 can be oriented in an upright orientation asillustrated in FIG. 13. More particularly, at least about 55% of thetotal number of shaped abrasive particles 1305 of the abrasive article1300 can be oriented in an upright orientation. Still, in otherinstances, the percentage can be greater, such as at least about 60%, atleast about 70%, at least about 80%, at least about 90%, or even atleast about 95% of all shaped abrasive particles 1305 of the coatedabrasive can have an upright orientation.

After sufficiently forming the make coat 1303 with the abrasiveparticulate material 1306, the size coat 1309 can be formed to overlieand bond the abrasive particulate material 1306 in place. The size coat1309 can include an organic material, may be made essentially of apolymeric material, and notably, can use polyesters, epoxy resins,polyurethanes, polyamides, polyacrylates, polymethacrylates, poly vinylchlorides, polyethylene, polysiloxane, silicones, cellulose acetates,nitrocellulose, natural rubber, starch, shellac, and mixtures thereof.

The process of forming the abrasive particles of embodiments herein caninclude formation of the abrasive particles from a mixture. The mixturecan be a mixture having certain materials and rheologicalcharacteristics that facilitate formation of the shape abrasiveparticles according to the embodiments herein. In certain instances, themixture can be a slurry or gel. For example, the mixture can include amixture of solid particles suspended in a liquid vehicle. In moreparticular embodiments, the mixture can be a sol gel includingparticulate matter mixed with a liquid vehicle, wherein the sol gelslurry comprises certain rheological characteristics, such that it is inthe form of a dimensionally stable mixture. In particular, the mixturecan be a gel formed of a ceramic powder material and a liquid, whereinthe gel can be characterized as a shape-stable material having theability to hold a given shape even in the green (i.e., unfired) state.In accordance with an embodiment, the gel can be formed of the ceramicpowder material as an integrated network of discrete particles.

For example, the mixture can include an abrasive precursor material. Anabrasive precursor material may be a material that can be formed into anabrasive particulate material through further processing, which mayinclude for example, a process such as calcining. In accordance with anembodiment, the mixture can include an abrasive precursor that includesmaterial such as oxides, borides, nitrides, carbides, oxynitrides,oxyborides, hydroxides, precipitated salts of nitrates, chlorides,sulphates, and a combination thereof. In particular instances, theabrasive precursor can include an alumina-based material, such asboehmite.

The term “boehmite” is generally used herein to denote alumina hydratesincluding mineral boehmite, typically being Al₂O₃.H₂O and having a watercontent on the order of 15%, as well as psuedoboehmite, having a watercontent higher than 15%, such as 20-38% by weight. It is noted thatboehmite (including psuedoboehmite) has a particular and identifiablecrystal structure, and accordingly unique X-ray diffraction pattern, andas such, is distinguished from other aluminous materials including otherhydrated aluminas such as ATH (aluminum trihydroxide) a common precursormaterial used herein for the fabrication of boehmite particulatematerials.

The mixture can be formed to have a particular content of solidmaterials. For example, the mixture can be formed such that it includesat least about 5 wt % solids for the total weight of the mixture. Inother instances, the amount of solids within the mixture can be greater,such as at least about 8%, at least about 10 wt %, at least about 12 wt%, at least about 15 wt %, at least about 18 wt %, at least about 20 wt%, at least about 25 wt %, at least about 30 wt %, at least about 35 wt%, at least about 40 wt %, at least about 50 wt %, or even at leastabout 55 wt %. Still, in particular instances, the solids content of themixture can be not greater than about 90 wt %, such as not greater thanabout 85 wt %, not greater than about 75 wt %, not greater than about 70wt %, not greater than about 65 wt %, not greater than about 55 wt %, oreven not greater than about 50 wt % for the total weight of the mixture.It will be appreciated that the mixture can contain a solids contentwithin a range between any of the minimum and maximum percentages notedabove.

Moreover, the content of abrasive precursor material that makes up thetotal solid content of the abrasive mixture can be controlled. Forexample, the amount of abrasive precursor material can be at least about40 wt % for the total weight of solids within the mixture. In otherinstances, the amount of abrasive precursor material for the totalamount of solid material can be greater, such as at least about 42 wt %,at least about 46 wt % at least about 50 wt %, at least about 55 wt %,at least about 60 wt %, at least about 70 wt %, at least about 80 wt %,at least about 85 wt %, at least about 90 wt %, at least about 95 wt %,or even at least about 97 wt % of the total weight of the solids withinthe mixture. Certain slurries can be formed such that essentially theentire weight of solid material is abrasive precursor material.

In accordance with another embodiment the mixture can include a certaincontent of abrasive grains Abrasive grains are distinct from abrasiveprecursor material, as abrasive grains represent the finally-formedphase of abrasive grains. For certain slurries, the abrasive grains maybe present as a seed material, which may facilitate a phase change ofabrasive precursor material also included within the mixture duringlater processing.

In some instances, the mixture can contain a minor amount of abrasivegrains, including for example, less than about 20 wt %, less than about10 wt %, or even less than about 5 wt %.

However, particular slurries can be formed such that they contain agreater content of abrasive grains. For example, a mixture can contain amajority content of abrasive grains. Notably, the mixture can contain acontent of abrasive grains that is the same as the content of abrasiveprecursor material for the total weight of solids within the mixture asnoted above.

The abrasive grains can include materials such as oxides, borides,nitrides, carbides, oxynitrides, oxyborides, diamond, and a combinationthereof. Certain abrasive grains include alumina, silicon carbide,alumina/zirconia and cubic boron nitride (i.e. cBN). In more particularinstances, the mixture can include abrasive grains that are made ofalumina, and more particularly, may consist essentially of alumina. Inone instance, the abrasive grains consist essentially of alpha alumina.It is to be understood however that the invention is not so limited butis capable of being adapted for use with a plurality of differentabrasive materials.

The mixture may contain a certain content of solid material, liquidmaterial, and additives such that it has suitable rheologicalcharacteristics for use with the process detailed herein. That is, incertain instances, the mixture can have a certain viscosity, and moreparticularly, suitable rheological characteristics that form adimensionally stable phase of material that can be formed through theprocess as noted herein. A dimensionally stable phase of material is amaterial that can be formed to have a particular shape and maintain theshape such that the shape is present in the finally-formed object.

Furthermore, the mixture can be formed to have a particular content ofliquid material. Some suitable liquids may include organic materials,such as water. In accordance with one embodiment, the mixture can beformed to have a liquid content less than the solids content of themixture. In more particular instances, the mixture can have a liquidcontent of at least about 25 wt % for the total weight of the mixture.In other instances, the amount of liquid within the mixture can begreater, such as at least about 35 wt %, at least about 45 wt %, atleast about 50 wt %, or even at least about 58 wt %. Still, in at leastone non-limiting embodiment, the liquid content of the mixture can benot greater than about 75 wt %, such as not greater than about 70 wt %,not greater than about 65 wt %, not greater than about 60 wt %, or evennot greater than about 65 wt %. It will be appreciated that the contentof the liquid in the mixture can be within a range between any of theminimum and maximum percentages noted above.

Furthermore, to facilitate processing and forming shaped abrasiveparticles according to embodiments herein, the mixture can have aparticular storage modulus. For example, the mixture can have a storagemodulus of at least about 1×10⁴ Pa, such as at least about 4×10⁴ Pa, oreven at least about 5×10⁴ Pa. However, in at least one non-limitingembodiment, the mixture may have a storage modulus of not greater thanabout 1×10⁷ Pa, such as not greater than about 1×10⁶ Pa. It will beappreciated that the storage modulus of the mixture can be within arange between any of the minimum and maximum values noted above. Thestorage modulus can be measured via a parallel plate system using ARESor AR-G2 rotational rheometers, with Peltier plate temperature controlsystems. For testing, the mixture can be extruded within a gap betweentwo plates that are set to be approximately 8 mm apart from each other.After extruding the get into the gap, the distance between the twoplates defining the gap is reduced to 2 mm until the mixture completelyfills the gap between the plates. After wiping away excess mixture, thegap is decreased by 0.1 mm and the test is initiated. The test is anoscillation strain sweep test conducted with instrument settings of astrain range between 01% to 100%, at 6.28 rad/s (1 Hz), using 25-mmparallel plate and recording 10 points per decade. Within 1 hour afterthe test completes, lower the gap again by 0.1 mm and repeat the test.The test can be repeated at least 6 times. The first test may differfrom the second and third tests. Only the results from the second andthird tests for each specimen should be reported.

Moreover, the mixture can be formed to have a particular content oforganic materials, including for example, organic additives that can bedistinct from the liquid, to facilitate processing and formation ofshaped abrasive particles according to the embodiments herein. Somesuitable organic additives can include stabilizers, binders, such asfructose, sucrose, lactose, glucose, UV curable resins, and the like.

Moreover, the mixture can be formed to have a particular content of acidor base distinct from the liquid, to facilitate processing and formationof shaped abrasive particles according to the embodiments herein. Somesuitable acids or bases can include nitric acid, sulfuric acid, citricacid, chloric acid, tartaric acid, phosphoric acid, ammonium nitrate,ammonium citrate. According to one particular embodiment, the mixturecan have a pH of less than about 5, and more particularly, within arange between about 2 and about 4, using a nitric acid additive.

In accordance with an embodiment, the process of forming the abrasiveparticles of the embodiments herein includes a process of forming themixture into a particular shape. Some suitable forming methods caninclude molding, extruding, casting, printing, rolling, stamping,punching, swiping, blading, and a combination thereof. In one particularinstance, the process of forming the mixture into a shaped abrasiveparticle having the features of the embodiments herein can includedepositing the mixture onto a substrate. Deposition of the mixture ontoa substrate can include a printing process, and more particularly, ascreen printing process.

FIG. 11 includes a diagram of a screen printing process in accordancewith an embodiment. As illustrated, the process of forming an abrasivearticle can include providing a mixture on a surface of a substrate1101, which may also be referred to as a belt. Notably, the substrate1101 can be translated between spools 1102 and 1103, such that thesubstrate 1101 can act as a conveyor belt, configured to translate thethrough certain processes, which facilitates the formation of theabrasive particles 1150. In accordance with an embodiment, the substrate1101 can be translated relative to a deposition region where the mixturecan be placed on the surface of the substrate 1101.

While not illustrated in particular, the screen printing system canutilize a die having a reservoir configured to contain the mixture to beprinted and formed into shaped abrasive particles. The mixture may beplaced under a force (or pressure) to facilitate extrusion of themixture through a die opening and into openings in a printing screen1107 and onto the translating substrate 1101 underlying the printingscreen 1107.

The printing screen 1107 can have a plurality of openings extendingthrough the volume of the substrate 1101. In accordance with anembodiment, the openings can have a two-dimensional shape as viewed in aplane defined by the length (l) and width (w) of the substrate 1101 thatinclude various shapes, for example, polygons, ellipsoids, numerals,Greek alphabet letters, Latin alphabet letters, Russian alphabetcharacters, complex shapes including a combination of polygonal shapes,and a combination thereof. In particular instances, the openings mayhave two-dimensional polygonal shapes such as, a triangle, a rectangle,a quadrilateral, a pentagon, a hexagon, a heptagon, an octagon, anonagon, a decagon, and a combination thereof.

After forcing the mixture through the die opening and through theopenings in the printing screen 1107, precursor shaped abrasiveparticles may be printed on a substrate 1101 disposed under the printingscreen 1107. According to a particular embodiment, the precursor shapedabrasive particles 423 can have a shape substantially replicating theshape of the openings, and at least a two-dimensional shapesubstantially replicating the shape of the openings as viewed in a planedefined by the length and width of the printing screen 1107. Notably,the average residence time of the mixture within the openings of theprinting screen 1107 can be less than about 2 minutes, less than about 1minute, less than about 40 second, or even less than about 20 seconds.In one non-limiting embodiment, the mixture may be substantiallyunaltered during printing, and more particularly, may experience noappreciable loss of volatile materials or drying in the openings of theprinting screen 1107.

The mixture can be deposited through an aperture and onto the substrate1101 in the manner of a screen printing process, as illustrated in FIG.11. Some particulars of the screen printing process are provided in U.S.Pat. No. 6,054,093, which is incorporated in its entirety herein.

In particular, the screen printing process can utilize a printing screen1107 in the form of a continuous printing belt that can pass around aseries of rolls 1108, 1109, 1110, and 111, with the space betweencertain rolls defining zones within the printing process. For example,the screen printing process can utilize an application zone, adisengagement zone, a cleaning zone, and a treatment zone. In theapplication zone, defined as the region between the rolls 1110 and 1111,the screen can be held in firm contact with the substrate 1101 while thescreen and the substrate 1101 move in the same direction at essentiallythe same speed and the mixture is applied to the inside surface of thescreen, ahead of a doctor blade 1112. The passage beneath the doctorblade 1112 forces the mixture into the apertures in the screen printingbelt, which at that point, is in firm contact with the substrate 1101.While a doctor blade 1112 is illustrated, in certain instances, a doctorblade may not be used.

In the disengagement zone between the rolls 1110 and 1109, the screenprinting belt can be disengaged from the substrate 1101 leaving thescreen printed shapes 1140 on the surface of the substrate 1101.

After extruding the mixture through the openings of the screen 1107, thesubstrate 1101 and screen 1107 may be translated to a disengagementzone, wherein the belt 109 and screen 151 can be separated from eachother to facilitate the formation of precursor shaped abrasiveparticles. In accordance with an embodiment, the screen 151 and belt 109may be separated from each other within the disengagement zone at aparticular release angle. In accordance with specific embodiment, therelease angle can be a measure of the angle between a lower surface ofthe screen 1107 and an upper surface of the belt 1101.

In accordance with an embodiment, the release angle may be particularlycontrolled to facilitate suitable formation of shaped abrasive particleshaving one or a combination of features described herein. For example,in accordance with an embodiment, the release angle can be at leastabout 15° and not greater than about 45°. In more particular instances,the release angle may be at least about 18°, such as at least about 20°,at least about 22°, at least about 24°, or even at least about 26°.Still, however the release angle may be not greater than about 42°, suchas not greater than about 40°, not greater than about 38°, or even notgreater than about 36°. It will be appreciated that the release anglecan be within a range between any of the minimum and maximum valuesnoted above.

The shapes 1140 can be transported by the substrate 1101 to furtherprocessing zones, including for example processing zone 1135. Certainsuitable processes, which can be undertaken in the processing zone 1135can include drying, heating, curing, reacting, radiating, mixing,stirring, agitating, planarizing, calcining, sintering, comminuting,sieving, and a combination thereof. In one particular embodiment, theprocessing zone 1135 includes a drying process, wherein moisture iswithdrawn from the shapes 1140 to improve the structural integrity ofthe particles for handling and further processing.

Meanwhile the screen printing belt 1107, after leaving the disengagementzone, can pass through a cleaning zone between the rolls 1109 and 1108.In the cleaning zone, the screen printing belt 1107 can be cleaned andreadied for use again. The cleaning process can include drying, directedbrushes, air blasts, and combinations of such processes.

From the cleaning zone, the screen printing belt can pass to thetreatment zone, in which a release agent may, if desired, be applied toease the separation of the shapes 1140 from the screen printing belt1107 in the disengagement zone.

Before the substrate 1101 enters the application zone in contact withthe screen printing belt 1107, it may be given a release treatment,(such a fluorocarbon spray), if the substrate 1101 has not beenpre-treated to give it a baked-on release layer.

As illustrated, after conducting the forming process, the shapes 1140can be transported by the substrate 1101 to the processing zone 1135. Inaddition to the processes noted above, the shapes 1140 can be treatedwithin the processing zone 1135 utilizing one or more processes such asdrying, heating, curing, reacting, radiating, mixing, stirring,agitating, planarizing, calcining, sintering, comminuting, sieving,texturing, and a combination thereof. In one particular instance, thetreating process can include a process that changes the rheology of themixture. The process of changing the rheology of the mixture canfacilitate the formation of a dimensionally stable phase of materialsuch that the texture formed in the mixture is maintained and part ofthe finally-formed abrasive particles 1150.

Certain processes, such as drying, heating, curing, calcining, andsintering, may be conducted to remove liquid materials from the mixtureand solidify and stiffen the shapes 1140. According to at least oneembodiment, the treating process includes texturing at least one surfaceof the shapes 1140 to form textured features in the finally-formedabrasive particles. Furthermore, a process of comminuting (i.e.,crushing) may also be undertaken to facilitate the formation of thefinally-formed abrasive particles 113.

The abrasive particles of the embodiments herein include features thatcan be formed using modifications to certain forming processes. Forexample, the abrasive grains can be formed to have one or a combinationof features disclosed herein utilizing a modification to the screenprinting process, wherein modifications to the process impart particularfeatures to the abrasive particles. For example, during printing, thescreen can be moved in a particular manner to form features, such as thetilted upper surface of the abrasive particles herein. In accordancewith an embodiment, the process of printing can include lifting thescreen at an angle relative to the planar surface of the substrate onwhich the mixture is printed. In particular instances, the screen canalso be lifted in a twisting manner relative to the planar surface ofthe substrate to form the tilted upper surface of the abrasive particlesherein. Notably, in such embodiments, the mixture can be in the form ofa dimensionally stable mixture wherein features provided to the mixtureduring forming are maintained throughout processing.

In addition to the process of printing the particles to form thefeatures noted herein, further processing can be conducted on theabrasive particles. For example, a process of texturing can be conductedafter forming the abrasive particles to facilitate formation of texturewithin the upper surface, and/or any other surfaces of the abrasiveparticles herein. Certain suitable texturing operations can includeembossing, etching, thermal treatment, radiation treatment, chemicaltreatment, sonic treatment, magnetic treatment, molding, pressing,punching, and a combination thereof. In particular instances, the shapes1140 can be textured by contacting a texturing form to a surface of theshapes 1140. Texturing using a texturing form can include processes suchas rolling, stamping, punching, swiping, blading, and a combinationthereof.

Notably, the abrasive particles of the embodiments herein utilize acombination of features not recognized or utilized in conventionalabrasive particles. Such features include, particular polyhedral shapes,contour of sides of the abrasive particles, variations in height andwidth of the abrasive particles, textured surfaces, and a combinationthereof. Moreover, the embodiments herein can utilize particular formingprocesses to facilitate the formation of abrasive grains having one or acombination of the features noted above. The combination of featuresfacilitates resilient abrasive particles that can readily beincorporated into a wide variety of abrasive articles, including coatedabrasive articles and/or bonded abrasive articles. The description isnot intended to set forth a hierarchy of features, but differentfeatures that can be combined in one or more manners to define theinvention.

Example 1

A first batch of shaped abrasive particles are made using a screenprinting process. A mixture, which is in the form of a gel, is initiallymade including 42 wt % boehmite commercially available as Catapal B fromSasol Corporation, 1 wt % sub-micron alpha alumina with respect to finalalpha alumina content in the body wherein the sub-micron alpha aluminahas a BET surface area greater than 120 m²/g and 2 to 4 wt % nitricacid. The mixture is extruded through a die opening and through a screenhaving triangular shaped openings. The triangular shaped openings have aside length of 2.38 mm and a depth of 625 microns minimum. No releaseagent is provided on the interior surfaces of the screen that define theopenings. The screen was moved at a rate of approximately 1 feet/min andwas released from the underlying belt at an angle of approximately 10°to 60°. The approximate resident time of the mixture in the openings isless than 10 seconds. Shaped abrasive precursor particles are formed onthe belt underlying the screen and then dried at a temperature of 95° C.for a duration of approximately 4-7 minutes. The dried particles aregathered and calcined at a temperature of 1000° C. for a duration of 10min and then sintered at a temperature of approximately 1300° C. for aduration of 10 to 30 min. The finally-formed shaped abrasive particlesconsist essentially of alpha alumina and have a median crystal size of0.1 to 0.5 microns, and particle size of 1.3 to 1.5 mm in length.

A first sample (S1) of randomly selected shaped abrasive particles istaken from the batch and analyzed via using a STIL (Sciences etTechniques Industrielles de la Lumiere—France) Micro Measure 3D SurfaceProfilometer (white light (LED) chromatic aberration technique) todetermine the average height difference, normalized height difference,and height variation. Each of the shaped abrasive particles of thesample are analyzed and the dimensions (i.e., h1 and h2) are recorded.FIGS. 14A-14J provide profilometer scans of each of the shaped abrasiveparticles of sample 1. The average height difference for sample S1 isapproximately 114 microns, the height variation is approximately 120,and the normalized height difference approximately 81. The averageprofile length of the first sample is calculated to be approximately 1.3mm, and thus the profile ratio of the sample is 0.088 (i.e.,[0.114/1.3]).

Example 2

A second batch is made according to Example 1, except that thefinally-formed shaped abrasive particles have a median particle size of1.2 to 1.5 mm in length.

A second sample (S2) of randomly selected shaped abrasive particles istaken from the second batch and analyzed via using a STIL (Sciences etTechniques Industrielles de la Lumiere—France) Micro Measure 3D SurfaceProfilometer (white light (LED) chromatic aberration technique) todetermine the average height difference, normalized height difference,and height variation. Each of the shaped abrasive particles of thesample are analyzed and the dimensions (i.e., h1 and h2) are recorded.FIGS. 15A-15J provide profilometer scans of each of the shaped abrasiveparticles of sample 2. The average height difference for sample S2 isabout 82 microns, the height variation is approximately 48, and thenormalized height difference is approximately 66. The average profilelength of the sample is calculated to be approximately 1.2 mm, and thusthe profile ratio of the sample is 0.068 (i.e., [0.082/1.2]). FIG. 19includes a picture of actual shaped abrasive particles formed accordingto Example 2. Notably, the shaped abrasive particles of FIG. 19 havegenerally triangular two-dimensional shapes, demonstrate ellipsoidregions within the upper surfaces, and further demonstrate significantheight difference features across their upper surfaces.

Example 3

Shaped abrasive grains available from 3M were obtained to conductcomparative analysis. A first comparative sample (CS3) is available asCubitron I having an average grit size of 36+. A second comparativesample (CS4) is available as Cubitron II having an average grit size of60+. A third comparative sample (CS5) is available as Cubitron II havingan average grit size of 80+. Each of the shaped abrasive particles ofsample CS3 are analyzed and the dimensions (i.e., h1 and h2) arerecorded. The average height difference for sample CS3 is about 40microns, the height variation is approximately 27, and the normalizedheight difference is approximately 33. In one analysis, the averageprofile length of the sample is calculated to be approximately 1.2 mm,and thus the profile ratio of the sample is 0.033 (i.e., [0.040/1.2]).In another analysis, the average profile length of the sample isapproximately 1.4 mm, and thus the profile ratio of the sample is 0.028(i.e., [0.040/1.4]).

Each of the shaped abrasive particles of sample CS4 are analyzed and thedimensions (i.e., h1 and h2) are recorded. FIGS. 16A-16J provideprofilometer scans of each of the shaped abrasive particles of sampleCS4. The average height difference for sample CS4 is about 30 microns,the height variation is approximately 18, and the normalized heightdifference is approximately 23. The average profile length of the sampleis calculated to be approximately 0.65 mm, and thus the profile ratio ofthe sample is 0.028 (i.e., [0.018/0.65]).

The shaped abrasive particles of sample CS5 are analyzed and thedimensions (i.e., h1 and h2) are recorded. FIGS. 17A-17J provideprofilometer scans of each of the shaped abrasive particles of sampleCS5. The average height difference for sample CS5 is about 17 microns,the height variation is approximately 11, and the normalized heightdifference is approximately 14. The average profile length of the sampleis calculated to be approximately 0.50 mm, and thus the profile ratio ofthe sample is 0.022 (i.e., [0.011/0.50]).

Clearly, upon comparison of the figures and data, the shaped abrasivegrains of the comparative examples are significantly different in termsof height variation. In fact, upon inspection, it is evident that thecomparative shaped abrasive particles are not formed to achieve heightvariation between ends of the particles, and rather “shape correctness”appears to be the preferred focus.

Example 5

The shaped abrasive particles of S1 and comparative shaped abrasiveparticles of sample CS3 tested in a single grit scratch test. The shapedabrasive particles are laid on their bottom surface, which is a majorsurface having the greatest surface area. For the shaped abrasiveparticles of sample S1, the particles are oriented in an uprightposition, representative of a preferred orientation for use in anabrasive article. In a single grit (i.e., shaped abrasive particle)scratch test, a single grit is held in a grit holder by a bondingmaterial of epoxy. The grit is moved across a workpiece of 304 stainlesssteel for a scratch length of 8 inches using a wheel speed of 22 m/s andan initial scratch depth of 30 microns. The grit produces a groove inthe workpiece having a cross-sectional area (A_(R)). Each shapedabrasive particle completes 15 passes across the 8 inch length, for eachsample 10 individual particles are tested and the results are analyzedand averaged. The change in the cross-sectional area of the groove frombeginning to the end of the scratch length is measured to determine thegrit wear.

FIGS. 18A and 18B provide the test results of a single grit scratchingtest. Clearly, and quite unexpectedly, the shaped abrasive particles ofthe embodiments herein demonstrated significantly improved performanceover the comparative sample. Notably, in terms of the measured percentgross fracture, the shaped abrasive particles of sample S1 demonstrateda 300% improvement over the comparative sample. Additionally, withrespect to the measured fracture level, the shaped abrasive particles ofthe embodiments herein demonstrated a significant improvement over theshaped abrasive particles of the comparative example. In particular, theshaped abrasive particles of sample S1 had a 50% reduction in fracturesper pass over the comparative sample. Moreover, the shaped abrasiveparticles of sample S1 had nearly a 100% improvement of 90^(th)percentile fracture level (N) over the comparative sample.

In the foregoing, reference to specific embodiments and the connectionsof certain components is illustrative. It will be appreciated thatreference to components as being coupled or connected is intended todisclose either direct connection between said components or indirectconnection through one or more intervening components as will beappreciated to carry out the methods as discussed herein. As such, theabove-disclosed subject matter is to be considered illustrative, and notrestrictive, and the appended claims are intended to cover all suchmodifications, enhancements, and other embodiments, which fall withinthe true scope of the present invention. Thus, to the maximum extentallowed by law, the scope of the present invention is to be determinedby the broadest permissible interpretation of the following claims andtheir equivalents, and shall not be restricted or limited by theforegoing detailed description.

The Abstract of the Disclosure is provided to comply with Patent Law andis submitted with the understanding that it will not be used tointerpret or limit the scope or meaning of the claims. In addition, inthe foregoing Detailed Description, various features may be groupedtogether or described in a single embodiment for the purpose ofstreamlining the disclosure. This disclosure is not to be interpreted asreflecting an intention that the claimed embodiments require morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive subject matter may be directed toless than all features of any of the disclosed embodiments. Thus, thefollowing claims are incorporated into the Detailed Description, witheach claim standing on its own as defining separately claimed subjectmatter.

What is claimed is:
 1. An abrasive article comprising: a shaped abrasive particle comprising a body having a first height (h1) at a first end of the body defining a corner between an upper surface, a first side surface, and a second side surface, and a second height (h2) at a second end of the body opposite the first end defining an edge between the upper surface and a third side surface, wherein the body comprises a normalized height difference defined by the equation [(h1−h2)/(h1/h2)] of at least about 40 microns, wherein h1 is greater than h2; wherein at least a portion of the upper surface has a curvilinear contour; and wherein the body comprises a bottom surface opposite the upper surface and having a substantially planar contour, wherein the bottom surface has a greater surface area relative to the upper surface.
 2. The abrasive article of claim 1, wherein the bottom surface comprises a surface area defined as a bottom area (Ab) and the body has a cross-sectional midpoint area (Am) defining an area of a plane perpendicular to the bottom area and extending through a midpoint of the shaped abrasive particle, and wherein the body comprises an area ratio of bottom area to midpoint area (Ab/Am) of not greater than about
 6. 3. The abrasive article of claim 1, wherein the body comprises a normalized height difference of at least about 43 microns.
 4. The abrasive article of claim 1, wherein the body comprises a normalized height difference of not greater than about 200 microns.
 5. The abrasive article of claim 1, wherein an average difference in height between the first height and the second height is at least about 50 microns.
 6. The abrasive article of claim 5, wherein the average difference in height is not greater than about 300 microns.
 7. The abrasive article of claim 1, wherein the body comprises a length and a width, and wherein the body comprises a primary aspect ratio of length:width of at least about 1:1 and not greater than about 10:1.
 8. The abrasive article of claim 7, wherein the body comprises a height, and wherein the body comprises a secondary aspect ratio defined by a ratio of width:height within a range between about 5:1 and about 1:3.
 9. The abrasive article of claim 8, wherein the body comprises a tertiary aspect ratio defined by a ratio of length:height within a range between about 6:1 and about 1.5:1.
 10. The abrasive article of claim 1, wherein the shaped abrasive particle comprises an average difference in height [h1−h2] and a profile length (l_(p)), and wherein the shaped abrasive particle comprises a profile ratio defined by the equation [(h1−h2)/(l_(p))] of not greater than about 0.3.
 11. The abrasive article of claim 1, wherein the shaped abrasive particle is part of a sample of shaped abrasive particles comprising a plurality of individual shaped abrasive particles, each individual shaped abrasive particle having a body having a first height (h1) at a first end of the body and a second height (h2) at a second end of the body opposite the first end, wherein h1 and h2 are significantly different relative to each other, and wherein the sample comprises a height variation of at least about 20 microns.
 12. The abrasive article of claim 11, wherein the sample comprises at least about 5 randomly-selected shaped abrasive particles made in a single forming process.
 13. The abrasive article of claim 11, wherein the height variation is not greater than about 180 microns, not greater than about 150 microns, not greater than about 130 microns.
 14. The abrasive article of claim 1, wherein the body comprises a rake angle defined as the angle between the first side surface and the bottom surface and wherein the rake angle comprises a value within a range between about 1° and about 80°.
 15. The abrasive article of claim 1, wherein the body comprises a substantially trapezoidal two-dimensional shape as viewed in a plane defined by a length and a width of the body.
 16. The abrasive article of claim 1, wherein the body comprises a polycrystalline material.
 17. The abrasive article of claim 1, wherein the body comprises a triangular two-dimensional shape as viewed in a plane defined by a length and a width of the body.
 18. The abrasive article of claim 1, wherein the body comprises abrasive grains selected from the group of materials consisting of nitrides, oxides, carbides, borides, oxynitrides, diamond, and a combination thereof.
 19. The abrasive article of claim 1, wherein the shaped abrasive particle is incorporated into a coated abrasive article or a bonded abrasive article.
 20. The abrasive article of claim 19, wherein the shaped abrasive particle is applied to a substrate of the coated abrasive article.
 21. The abrasive article of claim 1, wherein the upper surface comprises at least one depression. 